Differentiability and Limits

Please see the attached file for the fully formatted problems. Let f: I →ℜ where I is an open interval containing the point c, and let k ∈ ℜ. Prove the following 1. f is differentiable at c with f ′(x) = k iff lim h→0 [f(c+h) - f(c)]/h=k 2. If f is differentiable at c with f ′(c) = ...continues

Number Theory

Find all the integers such that when the final digit is deleted the new integer divides the original one. Can you generalize this to deleting other digits?

Quadratic equations

the problem is attached

Probability

The 'cup' system for determining the champion amongst 2^n players consists of drawing lots to arrange the players in 2^(n-1) pairs who are to play each other, then repeating this with the 2^(n-1) winners of these matches, and so on. The winner and loser of the final match receive the first and second prizes respectively. Suppose ...continues

Managerial Finance - capital management structure

What is the objective of the capital management structure?

Managerial Finance - expected returns

If a company's beta were to double, would its expected return double?

Managerial Finance - business cycle

Why should the financial manager be familiar with the business cycle?

Quadratic equations

See attached

LIFO and FIFO inventory methods

With inflation, what are the implications of using LIFO and FIFO inventory methods? How do they affect the cost of goods sold?

Rapid corporate growth in sales and profits

Rapid corporate growth in sales and profits can cause financing problems. Elaborate on this statement.